Is a block on one inclined plane the most boring physics problem ever? possibly not.Is a block on one inclined aircraft the most boring physics trouble ever? maybe not. Rhett Allain
It's maybe the 2nd week of her introductory physics course. Her instructor beginning talking about friction and writes the complying with two formulas on the board.
You are watching: Does the coefficient of kinetic friction depend on the weight of the block
Then over there is probably some type of lecture choose this:
Friction is a call force as soon as two surface interact. The 2nd equation is the kinetic frictional pressure that is used when 2 surfaces room sliding versus each other. The frictional pressure in this case depends ~ above the two types of materials communicating (described by the coefficient μk) and how hard these two surfaces are moved together (the regular force). The static friction case is similar for when the two surfaces space stationary family member to every other. In revolution friction, the frictional pressure is everything value it needs to it is in to avoid sliding up to some preferably value.
Technically, this is referred to as Amontons' an initial and 2nd Law that Friction. See, it's not just Newton that has actually laws. Notification that both of these friction formulas just depend top top the coefficient that friction and also the typical force. It does not depend the area that contact, that doesn't rely on the slide speed.
Next, there will more than likely be some form of friction laboratory experiment. In this lab, students will measure coefficients that friction and also show that the frictional pressure doesn't count on surface ar area in contact. Also, the coefficient the friction doesn't depend on the fixed of the object. Pretty conventional stuff here.
Friction Is simply a Model
How about another experiment? In this experiment, i am going to put an object on an moveable plane. I have the right to then rise the edge of inclination until this block just starts to slide. In ~ the minute it starts to slide, I deserve to calculate both the normal pressure (pushing the plane against the object) and the friction force (the maximum static friction force).
Just in ~ the instant this point starts to slide, all of these forces still have to include up to the zero vector (object is in equilibrium). That way that the component of the gravitational pressure perpendicular come the airplane must be same to the size of the normal force and also the ingredient parallel to the plane must be same to the frictional force.
With just the mass and also the sliding angle, ns can gain both the friction force and the typical force. How have the right to I calculation the coefficient that friction? What if ns made a plot that friction vs. Normal pressure for the exact same surface yet with different masses? If the typical force and the frictional force are yes, really proportional (like in the version above) then this data should be direct with the slope of the heat being the coefficient the friction.
It's simple, right? Ok. Let's execute this. In order to keep everything the same other than for the mass, ns am walk to placed masses right into one the these small boxes.
This box has actually a teflon bottom with an open top for this reason you can put masses within (oh, it's indigenous PASCO). There is additionally a variable angle inclined plane. This one in details has a large angle measure on the side and here you deserve to see the friction box with a huge amount of fixed both inside and also on peak of it.
Actually, there is also a comparable plane the is do of metal rather of wood. I tried this experiment both v a felt-bottomed crate on wood and also a teflon crate on metal. Because that each mass, I slowly lifted the incline until package slipped and then tape-recorded the angle. I repetitive the experiment for the same mass 5 or 6 times so that I might get an median angle and also a standard deviation in the edge measurement.
Here is a plot the friction force vs. Normal force for both surfaces. The error bars room calculated (using the crank three times method) from the conventional deviation in edge measurements.
What's walking on here? Let's look in ~ the data because that the teflon (the blue data). Ns fit a linear function to the an initial 4 data points and also you have the right to see that is an extremely linear. The slope of this line provides a coefficient of static friction v a value of 0.235. However, together I add an ext and an ext mass to the friction box, the normal force keeps increasing however the friction force doesn't boost as much. The same thing happens for friction box with felt ~ above the bottom.
This reflects that the "standard" friction version is simply that - a model. Models were intended to it is in broken.
A an ext Detailed Look at Friction
Really, what is friction? You could say that when two surfaces come close to each other (call them surface ar A and also surface B), the atoms in surface ar B gain close enough to interact with surface A. The much more atoms the are interacting in the 2 surfaces, the better the total frictional force. Exactly how do girlfriend get more atoms to communicate from the two surfaces? Well, if you press the surfaces with each other you deserve to get much more atoms native A to be close sufficient to the atom from B come interact. Yes, ns am simplifying this a bit. However, the allude is that call area does undoubtedly matter.
I to be talking about contact area, not surface ar area. Suppose you put a rubber ball on a glass plate. Together you push down top top the rubber ball, it will certainly deform such that an ext of the ball will come in "contact" through the glass. Right here is a diagram of this.
Greater contact area means greater frictional force. If the call area is proportional come the normal force, then this looks similar to Amontons' legislation with the frictional force proportional to the common force. Of food this version "breaks" once the contact area can no longer increase. Together I add more and much more mass onto the friction box, over there is less and less available contact area to expand into. In a sense, the contact area becomes saturated. I mean that if I kept piling ~ above the weight, the friction force would at some point level out and stop increasing.
It's simply a Model
This yes, really isn't a big deal. The Amontons' law isn't a regulation at all (ok - it depends on your definition of Law). It's simply a model. A version is no THE TRUTH, it's just something the works few of the time. Allow me offer an example.
Gravitational Model. close to the surface ar of the Earth, we can calculate the gravitational force on an object using the following model.
The g vector is the regional gravitational field. Top top Earth, the points "down" and has a magnitude approximately 9.8 N/kg. We often speak to this gravitational pressure the weight and it's a an extremely useful model.
Even though this model is useful, us still understand it's wrong. The above gravitational model says the it doesn't matter just how high above the surface ar of the earth you are, the load is the same. Of food that's no true, however it's around true as soon as close come the surface.
Here is a far better gravitational model.
This claims that the gravitational force decreases as the two connecting objects get more away from every other. If you placed in the mass of the Earth and also the radius the the planet you get a weight that looks as with the mg version. So, at some point the two versions of heaviness agree.
The same is true because that friction. The introduce physics variation of friction functions for part stuff and a more complicated version that friction functions for various other cases. Of course you might still use the complex version the friction for simple cases - but why make her life difficult?
Rhett Allain is an combine professor the physics at Southeastern Louisiana University. He enjoys teaching and talking around physics. Sometimes he takes points apart and also can't put them earlier together.
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